Question

What is the 30th term of the arithmetic series 3, 5, 7, …?

Answer 1

61 is  the 30'th term of the sequence.

Answer 2

The nth term for the arithmetic sequence is given by:

`a_n = a_1+(n-1)d` .....[1]

where,

`a_1` is the first term.

d is the common difference.

n is the number of terms.

Given the sequence:

3, 5, 7, .......

This is an arithmetic sequence

First term (
`a_1`) = 3

Common difference(d) = 2

Since,

5-3 = 2,

7-5 = 2 and so o....

We have to find the 30th term of the given sequence:

Substitute n = 30 and the given values in [1] we have;

`a_(30) = 3+(30-1)(2)`

`a_(30) = 3+29 \cdot 2 = 3+58 = 61`

Therefore, the 30th term of the given sequence is, 61